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# A Novel Approach to Handle Inference in Discrete Markov Networks with Large Label Sets

*Proceedings of the Ninth International Conference on Probabilistic Graphical Models*, PMLR 72:249-259, 2018.

#### Abstract

MAP inference over discrete Markov networks with large label sets is often applied, e.g., in localizing multiple key points in the image domain. Often, approximate or domain specific methods are used to make the problem feasible. An alternative method is to preselect a limited (much smaller) set of suitable labels, which bears the risk to exclude the correct solution. To solve the latter problem, we propose a two-step approach: First, the reduced label sets are extended by a novel “refine” label, which — when chosen during inference — marks nodes where the label set is insufficient. The energies for this additional label are learned in conjunction with the network’s potential weights. Second, for all nodes marked with the “refine” label, additional local inference steps over the full label set are performed. This greedy refinement becomes feasible by extracting small subgraphs around the marked nodes and fixing all other nodes. We thoroughly evaluate and analyze our approach by solving the problem of localizing and identifying 16 posterior ribs in 2D chest radiographs.